“How easy it is to follow our thoughts instead of our senses.”
Frank Herbert

Children of Dune

Christopher Alexander – Fundamental Property 8: Deep Interlock and Ambiguity

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Images selected by me inspired by the ones shown in the book.

“In a surprisingly large number of cases, living structures contain some form of interlock: situations where centers are ‘hooked’ into their surroundings. This has the effect of making it difficult to disentangle the center from its surroundings.

… a similar unification is accomplished through the creation of spatial ambiguity … a common example … is the house with a gallery or arcade round it … the space in the gallery belongs to the outside world and yet simultaneously belongs to the building.”

Profound interlock in Inca stonework

Dovetail as an example of deep interlock

Tile-work and brick in the 16th centur Tabriz Mosque

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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Christopher Alexander – Fundamental Property 7: Local Symmetries

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“… Where a living center forms, it is often necessary to have some local symmetry.

… Living things, though often symmetrical, rarely have perfect symmetry. Indeed, perfect symmetry is often a mark of death in things, rather than life. I believe the lack of clarity on the subject has arisen because of a failure to distinguish overall symmetry from local symmetries.

… The Rorschach ink-blot, for instance, is a rather weak whole; it has relatively little life as a structure; its centers are poorly developed. The one large symmetry it has, by itself, gets you very little.

… over simplified symmetry in a building is mot often naive and even brutal … Albert Speer’s design for Zeppelinfeld … is [an] example …

In general, a large symmetry of the simplified neoclassicist type rarely contributes to the life of a thing, because in any complex whole in the world, there are nearly always complex, asymmetrical forces at work – matter of location, and context, and function – which require that symmetry be broken.

We see this clearly in the Alhambra … a marvel of living wholeness. It has no overall symmetry at all, but an amazing number of minor symmetries, which hold within limited pieces of the design, leaving the whole to be organic, flexible, adapted to the site.

… the real binding force which symmetry contributes to the formation of life is … in the binding together and local symmetry of smaller centers within the whole.

… an experiment I did … at Harvard Center for Cognitive Studies … I compared a number of black and white paper strips, and measured their coherence as felt, experienced, perceived, remembered, by different subjects.

… The experiments were performed with 35 black-and-white strips seen on a neutral gray background. Each strip was 7 squares long, and was composed of 3 black squares and 4 white squares, arranged in different arrangements …

First, we established that the relative coherence of the different patterns … is not an idiosyncratic subjective feature of the patterns seen differently by different people. It is an objective measure of cognitive processing, roughly the same for everyone.

Second, we were then able to identify the structural feature of these patterns which caused this perceived ‘coherence.’ It turned out that [it] … depends on the number of local symmetries present in the pattern. However since most of the symmetries are hidden, this feature is far from obvious …

… For three of four years after completing the experiment, I worked almost continuously to find some structural feature of the 35 black and white patterns which would explain the rank order of coherence of the different patterns …

… it was quite unclear how to unite the idea of symmetry with the idea of large lumps. It was this that finally gave me the key, when I realized that both overall symmetries and large lumps actually contain more local symmetries inside them.

.. the strips which are most coherent experimentally also have the highest number of subsymmetries to within a high degree of correlation … The number of local symmetries the pattern contains essentially predicts how ‘good’ it is.

… It is as if the symmetrical segments act as a kind of glue … which holds the space together. The more glue there is, the more the space is one, solid, unified, coherent. And … for the glue to be effective, it seems that many of the symmetrical segments must overlap.

… the local symmetries … though hidden from view … essentially control the way the pattern is seen and the way it works.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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Christopher Alexander – Fundamental Property 6: Good Shape

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Reading this section while thinking about creating the excerpt made me tense. I feel this property is tricky because it is so obvious and yet also so subtle and hard to pin down. When I create these excerpts I choose to share parts which feel clear and resonate for me (in the hope that my sense of clarity adds something to the being-ness of excerpt). This one was sticky. It was challenging for me (the first time around, the second time easier) and I expect it may be challenging for you. It demands that we look examine our likes (and dislikes). It is confrontational in that it dares to suggest that we’ve learned to like futuristic chairs; that they are empirically bad; and that if we want to learn to make living structures we are going to have to acknowledge this, reflect on these likes and we are going to have to unlearn them, to see past them, to restore a deeper, more subtle form of seeing. It is a tough ask.

The Copenhagen Police Headquarters was the only image specific enough to seek out and find on my own, the others felt too subtle and I could not find substitutes that felt good enough for me, so I scanned them from the book.

“When I began looking for living structures … I became aware of a special quality that I began to think of as good shape, but could not very easily explain it, or define it …

It took me a long time to see that good shape itself is also related to the centers … a shape we see as good it a shape which it itself, as a shape, made up from multiple coherent centers …

It it easiest to understand good shape as a recursive rule … the elements of any good shape are always good shapes themselves …

… the simplest and most elementary good shapes are from elementary figures … the good shape, no matter how complex, is built up from the simplest elementary figures. The teapot stand can be seen to be built up from the illustrated simple shapes, each of which has good shape …

On the other hand, the amorphous mass of the futuristic chair cannot be understood as being composed of elementary shapes at all.

… what seems like complex centers are made of simple centers which are also alive – and it is these centers above all which give the complex ones their life …

… The good shape is an attribute of the whole configuration, not of the parts; but it comes about when the whole is made of parts that are themselves whole in this rather simple geometric sense …

All in all, in my experience, in the build-up of a good shape the following elements are the most common: square, line, segment, arrowhead hook, triangle, row of dots, circle, rosette, diamond, S-shape, half-circle, star, steps, cross, waves, spiral …

All of this is subtle when we try to apply it. Take the circle, for instance … [it] has great problems. The space next to it is not easily made positive, not easily made into centers – and the circle, when used in a design can easily then not be good shape at all. We see such an example in the courtyard of the Copenhagen Police Headquarters: a ridiculous plan, which is trivial because the space next to the circle is formless, and therefore meaningless.

The high degree of sophistication needed to make a circle have good shape is seen in the fabulous Ottoman velvet … where the two systems of circles are drawn slightly distorted so that the moon shapes, the space between the circles, and the small circles and large circles all work as centers.

Although it may seem surprising to someone raised in the mechanist-functionalist tradition, good shape … is not only making things more beautiful; it also makes them work more profoundly, more effectively.

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

 

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Christopher Alexander – Fundamental Property 5: Positive Space

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“What I call positive space occurs when every bit of space swells outward, it substantial in itself, is ever the leftover from an adjacent space. We may see it like a ripening corn, each kernel swelling until it meets the others …

An almost archetypal example of this positive and coherent state of space may be seen in the 17th century Nolli plan of Rome. In this plan each bit of every street is positive, the building masses are positive, the public interiors are positive. There is virtually no part of the whole which does not have definite and positive shape. This has come about, I think, because of these spaces … has been shaped over time by people who cared about it, and it has therefore taken a definite, cared for shape with meaning and purpose …

In the present Western view … we tend to see buildings floating in empty space … the buildings … have their own definite physical shape – but the space which they are floating in is shapeless, making the buildings almost meaningless in their isolation. This has a devastating effect: it makes our social space itself – the glue and playground of our common public world – incoherent, almost non-existent …

Here in the famous Kizaemon tea bowl, now preserved in Japan … its beauty lies in the fact that not only does the bowl have a beautiful shape in itself, but that also the space next to the bowl has a beautiful shape. One might even say that the beauty of the bowl is created by the fact that the space next to it is beautiful.

… In Matisse’s cut-out blue nude, every part of the space is positive …

The definition of positive space is straightforward: every single part of space has positive shape as a center. There are no amorphous meaningless leftovers. every shape is a strong center, and every space is made up in such a way that it only has strong centers in its space, nothing else besides.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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Christopher Alexander – Fundamental Property 4: Repetition

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Once again, except for the dull office building facade (scanned from the book), the images are selected by me.

“… Centers intensify other centers by repeating. The rhythm of the repeating centers, slowly, like the beat of a drum, intensifies the field effect.

… Most things are made from repetition at some level: repetition of atoms, molecules, waves, cells, volumes, roofs, trusses, windows, bricks, columns, tiles, entrances and so on. But the repetition which occurs in things which have life is a very special kind of repetition … where the rhythm of the centers that repeat is underlined, and intensified, by an alternating rhythm interlocked with the first and where a second system of centers also repeats, in parallel. The second system of centers then intensifies the first system, by providing a kind of counterpoint, or opposing beat.

… Somehow the sense of order in a thing comes from the fact that elements are repeated … often the calmest life arises when a thing, like a basket, is made entirely out of one kind of smaller element repeating.

… repetition tends to be inexact; it is then the subtle variation which comes with the repetition that is satisfying and life giving. This happens because the elements are not identical, but modified each according to its position in the whole …

But there is a deeper aspect of the repetition. This concerns the fundamental character of the repetition and the way that elements are repeated: there is profound and satisfying repetition of living centers, and there is banal repetition of elements …

… the facade of a modern office building … Here the alternation is brutal, banal … what repeats is one dimensional: there is no alternation to speak of, no living centers … no vital secondary centers …

… in Brunelleschi’s Foundling Hospital, the round medallions alternate within the columns and column bays. We see the columns repeating … the arches repeating … space of bays repeating … triangular space between adjacent arches repeating … ceramic roundels in these triangles repeating … Each of these things … is a profoundly formed and living center. The result is beautifully harmonious and has life.

… it seems that what is really happening is not repetition, but oscillation … In the Ottoman velvet … the oscillation … has reached tremendous and profound subtlety.. The waves with the ‘lips’ oscillate. The triple circles oscillate. The space between circles and lips oscillates. The overall effect is a profound unity.

… The life comes about only when the alternating wholes are beautifully and subtly proportioned and differentiated.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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